{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exercícios\n",
    "\n",
    "1 - Aplique os algoritmos K-means [1] e AgglomerativeClustering [2] em qualquer dataset que você desejar (recomendação: iris). Compare os resultados utilizando métricas de avaliação de clusteres (completeness e homogeneity, por exemplo) [3].\n",
    "\n",
    "    [1] http://scikit-learn.org/stable/modules/clustering.html#k-means\n",
    "\n",
    "    [2] http://scikit-learn.org/0.17/modules/clustering.html#hierarchical-clustering\n",
    "\n",
    "    [3] http://scikit-learn.org/stable/modules/clustering.html#clustering-evaluation\n",
    "\n",
    "2 - Qual o valor de K (número de clusteres) você escolheu para a questão anterior? Desenvolva o Método do Cotovelo (não utilizar lib!) e descubra o K mais adequado. Após descobrir, aplique novamente o K-means com o K adequado.\n",
    "\n",
    "    Ajuda: atributos do k-means\n",
    "\n",
    "3 - Após a questão 2, você aplicou o algoritmo com K apropriado. Refaça o cálculo das métricas de acordo com os resultados de clusters obtidos com a questão anterior e verifique se o resultado melhorou.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn import decomposition\n",
    "from sklearn import metrics\n",
    "from sklearn.model_selection import train_test_split\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from sklearn.cluster import KMeans\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dataset = load_iris()\n",
    "X = dataset.data\n",
    "y = dataset.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "kmeans = KMeans(n_clusters=2, random_state=0).fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# kmeans.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions= kmeans.predict(X)\n",
    "# data = decomposition.PCA(n_components=2).fit_transform(X)\n",
    "data=kmeans.fit_transform(X)\n",
    "data_df = pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            0         1  2\n",
      "0    0.250176  4.089154  0\n",
      "1    0.418604  4.108307  0\n",
      "2    0.442488  4.276180  0\n",
      "3    0.494062  4.140016  0\n",
      "4    0.302729  4.135706  0\n",
      "5    0.691419  3.760009  0\n",
      "6    0.438849  4.215490  0\n",
      "7    0.115511  4.019571  0\n",
      "8    0.782921  4.303085  0\n",
      "9    0.344147  4.064270  0\n",
      "10   0.531590  3.959061  0\n",
      "11   0.230552  4.004449  0\n",
      "12   0.483836  4.180618  0\n",
      "13   0.936545  4.631831  0\n",
      "14   1.085906  4.225712  0\n",
      "15   1.256659  4.036578  0\n",
      "16   0.726547  4.111530  0\n",
      "17   0.234206  4.053640  0\n",
      "18   0.833352  3.709926  0\n",
      "19   0.454063  4.023467  0\n",
      "20   0.428846  3.732642  0\n",
      "21   0.374850  3.968178  0\n",
      "22   0.738908  4.616481  0\n",
      "23   0.275995  3.696354  0\n",
      "24   0.407180  3.756375  0\n",
      "25   0.373084  3.901855  0\n",
      "26   0.124170  3.862233  0\n",
      "27   0.262685  3.973565  0\n",
      "28   0.271167  4.047010  0\n",
      "29   0.358381  4.022494  0\n",
      "..        ...       ... ..\n",
      "120  4.978003  1.171061  1\n",
      "121  3.838797  0.771290  1\n",
      "122  6.074408  2.255884  1\n",
      "123  3.941571  0.221618  1\n",
      "124  4.824539  1.021189  1\n",
      "125  5.178652  1.414702  1\n",
      "126  3.808870  0.231849  1\n",
      "127  3.840836  0.259939  1\n",
      "128  4.673585  0.769282  1\n",
      "129  4.962153  1.240112  1\n",
      "130  5.406874  1.599788  1\n",
      "131  5.907857  2.358105  1\n",
      "132  4.713243  0.826208  1\n",
      "133  3.996525  0.256546  1\n",
      "134  4.394781  0.788213  1\n",
      "135  5.659134  1.907187  1\n",
      "136  4.736863  1.081923  1\n",
      "137  4.449925  0.599262  1\n",
      "138  3.726340  0.373533  1\n",
      "139  4.654613  0.873104  1\n",
      "140  4.868220  1.054368  1\n",
      "141  4.496366  0.888379  1\n",
      "142  4.022313  0.589462  1\n",
      "143  5.109475  1.264153  1\n",
      "144  4.988510  1.235364  1\n",
      "145  4.503242  0.771490  1\n",
      "146  4.102432  0.439120  1\n",
      "147  4.304029  0.450705  1\n",
      "148  4.494624  0.912932  1\n",
      "149  3.966028  0.452190  1\n",
      "\n",
      "[150 rows x 3 columns]\n"
     ]
    }
   ],
   "source": [
    "# print(predictions)\n",
    "# print(reduced)\n",
    "# print(reduced_data_df)\n",
    "data_df[2]=predictions\n",
    "print(data_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
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mwDC6uodPalBVlc5uN4GBgRerbCG+sICAALp7zxwq293jwhQ48W445I5bDGMw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\nONhe7OTu+wqxWq19cdXV3cmiN9aSnTGM4r0lVJ/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc24966e278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bzYarqysbNm/im8JCQhJGdl1nt9s5s2kz//nSD/Dx8aGk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\n6P8DBeFtl9pkNtEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc25122ddd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = map(lambda x: colmap[x+1], predictions)\n",
    "\n",
    "f, ax = plt.subplots()\n",
    "ax.scatter(data_df[0], data_df[1], c=reduced_data_df[2], alpha=0.5, edgecolor='k')\n",
    "plt.show()\n",
    "\n",
    "f, ax = plt.subplots()\n",
    "ax.scatter(reduced_data_df[0], reduced_data_df[1], c=y, alpha=0.5, edgecolor='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "AgglomerativeClustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tf5wfagijpqpmvEo+L+lxiyGZmZn84peP8vJLT7F993GSTzVxusWJKTSXDTdf\nf8HXm4Ij6O4Z/lCDqqp09XiYGxw8VmUL8bkFBQXhVs++Senw2AmLGLsnID8rCW4xjMFg4P4vfI3m\n5mY6OzspWBRJYmLiiG4u5ucX8JfHt5Ce2kFmRhQ+n8qBQw34NEnnnQMrxHhQVZWmpiba29uJiIgg\nNTWVqJRwapqrSY/PQEGhw9yO08/+qQ+sjRdFVdVRv2hBQYFaVFQ06tcVE19dXR1vvfkcbmcrbg/E\nJczg5vX3EhISMt6lCQEMTg185olnKC2qJEATiMNnI3V6MnfcfTubXt1M9ckaNIqGiLgw7nvwXtLT\n0y9JXYqiHFFVtWBE50pwi9Gmqipmsxm9Xj/siTQhJoKtb2/jw9d2kZc2G42iQVVVyhpKmH3tdO66\n+y56e3txu91ERkZe0mmsFxPccnNSjDpFUQgPD5fQFhPS3g/3kRGbjUYZjD9FUchKmML+nQfx+XyE\nhoYSFRU1oZ89kOAWQlxR3C4XWq122DGNRoPX42UsRiDGggS3EOKKMndRAfVtdcOO1bfVMXPujLMC\nfaK64KwSRVGSgOeBWMAHPKGq6u/HujAhhBgLa29YS2VZFcfrjxKoC8LusWKM1nPrHbeMd2kjdsGb\nk4qixAFxqqoeVRTFBBwBblZVtex8r5Gbk0KIiczlcnHixAlamlqIjo1m1qxZ+Pn5jWtNF3Nz8oI9\nblVVW4HWM38fUBSlHEgAzhvcQggxkRkMBgoKCmBEMTnxXNQYt6IoqcBs4NBYFCOEEOLCRhzciqIE\nAa8D31VVtf8cX39YUZQiRVGKOjs7R7NGIYQ4J4/HQ319PU1NTZNmRshoGNEj74qi6BkM7RdVVd18\nrnNUVX0CeAIGx7hHrUIhhDiHiooKnv3zc7j6PfjwEZEQype//tDQMq2Xswv2uJXBWehPA+Wqqv52\n7EsSQohPZzab+fPvniBOk8Ls5LnkJ81D1x3AY799HI/HM97ljbmRDJUsAu4DViiKUnzmz7k3LhRC\niEvg6NGj+LkCCQ8eXONdURQSo5Owdzmprq4e5+rG3khmlewFJu6zn0KIK47VYkWvOXtzDx167Hb7\nOFR0acmyrkKICau7u5sPd3xIdfkpouOiWHHNctLT08meks0Ozy58qm9ozRGXx4WNAVJTU8e36EtA\nglsIMSF1dXXx61/8D3pLANFhMbS2dfPbA7/n4e8/SG5uLjMWTuPY3kJiTHF4vB46HW1cd/vqK2KL\nPAlucdF8Ph/d3d0YDAZZZ1uMme3v7cBgDSI7eQoAYaZwTP3BvPbCRnL/K5cvPvRFTsw7wZHDRzEY\nDdx51Xqys7PHuepLQ4JbXJSfxNuTAAAgAElEQVTKykq2vvUcWsWMw+EjNmEG62+5j2DZmkyMsoqT\nFcRFJA47Fh4czqnGCgYGBggJCWH27NnMnj17nCocPxLcYsQ6Ozt5c/MfuP2mKFKSp+H1+th7oJpX\nXn6CLz/8g6H1i1VVpaSkhOJje3A6rGRmz2HBgoXjvhaEmFzCo8IZqBvAFPBxp8DpcqDVa/D39x/H\nysafLOsqRqyo6CAFM/WkJA+OIWq1GpYuSsNhraGlpWXovO3bt7Hnwz8wa+ppll9loat5I88+83tc\nrrM3YxXifK65bhVN/fUM2AYf1Ha5XZSdLmHptUswGM6eUXIlkR63GDHLQDdxScZhxxRFISJMz8DA\nAAD9/f0cLXybb315Cv7+g99cqSnhvPJ6BcePH2fu3LmXvG4xOaWkpBCXHcOLG/8KHg2R8RHcef/t\n3LTuxvEubdxJj1uMWFLyVCqqhi9TY7O5aGx2k5CQAEBTUxMpibqh0IbBcJ+WbaKxoeKS1ismL6/X\nyx9/9xj9NXbuWf1Fbl55K+nRmbS3tKHRSGzJJyBGbPbs2XT1JbBlayUNjT2UV7bxt1erKJh/09D+\nkkFBQfSYPWct+GPudRFkuvynaYnRUV5eTntNFzkpuZgCTMSGxzE7s4CG8mZOnTo13uWNOxkqESNm\nNBp58Ms/4MCBvWzfcwSjXziLl28gNzd36JykpCQ0hhT2H2zgqvnJaDQaGk/3cOSEmzs2TOe997ZS\nd6qYgMAQ5hQsJycnZ0JvyiouHY/HQ1lZGXWn6qhvqEfj1g37t6EoCv4E0N7eTlZW1jhWOv4kuMVF\n8ff3Z8WKa1ix4pqhY42NjRQfO4TTaSUrexZ33vUwb/z9bxw8Uo7RCB5fONde92Xe2PwMWSk9rF0R\nTf9ACx+9/3tOn17HsmUrrvhZAlc6h8PBY4/+iebyNkz6EFo7mzlZdZKkmJSh9UgAHNiJjIwcx0on\nBglu8bkcPLiP/bufZ35+AP6Reo4dOsDx4pl84YFv0t/fj8vlIioqit27d5Ia38111w4+TGGxDJA7\npYL/ffInHNo/l4ysedy0boPMB79C7d61m7byLmalFqAoCmnxGXQ1m9m6603uXHMPKHCquZqYjMgr\nvrcNMsYtPgebzcZHH7zEAxvSuGp+GrNmJHLfXdPwOo5TUlJCWFgYMTExaDQaTjeWMTU7DAC3y8WJ\n4/uZku5h1bJw7roljsSoCv723B/x+XyXvB0ul4vW1lb6+8/aH0RcIof3FZEYkTI0NKLVaFmz6jq0\n/hoOn97L8fZCcpdn863vfXPS7MQ+lqTHLT6zxsZGkuIUQkMDho5pNBpm5oZQU32CmTNnDh03mSLp\n7qkFoK29jYgwL5HhwfT19RIWGkBWRjSVNWXU1dWRkZFxydpw4MBedn20keBAN/0WL2kZV3Hz+g0Y\njcYLv1iMGr1Bj9c3fB1tg8FAZnYG//n7XxEUFCT3Qj5BetziMzMajVisZy9ab7O5MfoFDjs2d94S\n9hfZaWruxeGwYdApbN/ZQVRMLJERQQDEROnp7e29JLXD4A4qh/c/z0P3xPLVL03le1+bip9SyJY3\nX71kNYhBi5cvpLG7Hq/PO3SstrmG3DnTMZlMEtr/RIJbfGYpKSk43DGcKPn4qcmeHiuHjtqYPXv+\nsHMTEhK47oZvsPEtGy9t6uI//9BMryWGG9bk09dnx+VyU9vgGpoPfikUHv6Q5YvDCQ8f/CGj12u5\ndmUGNVX7sdlsl6wOAQsWLGDuNbM42niQ0sYTHG04jF+ylrvuuXO8S5uQZKhEfGYajYYN93ydV156\nnAOF5QT4a2jpUFh17ZfOGcC5ubnk5PwHbW1tvPjC45RXFlJW/gY6rcrpFg/TZqwnNjb2rNf5fD6a\nmprw+XwkJSWN2hinZaCH8LDhvxkYjToC/BVsNhsBAQHneaUYbVqtlnvvv5dV166iubmZ4OBgMjIy\n5GGb85DgFp9LTEwM3/rOzzh9+jROp5Pk5ORPXUxKo9EQHx9PYlIGncoJZuTEEOBvwEc4ew6dpqGh\ngZSUlKHzT58+zabX/oyfvgetVqHPEsjNtzw8KjMLklNzKa/8iPi4j5embW3rw+01ERYW9rmvLwZ1\ndnbS2dlJeHj4OX8wf1JsbOwFzxES3GIUaDSaYWF7IRaLhYbaw3z3q1djMHz8T1CrO82hgx+RkvIA\nMDjb4+UXf8+N1xqZkjUNgKrqdh759Y+YOWseoWHRzClY+pnXYF68eDlPPXEIr7eaKVkRdPdY2bW/\nn1WrvyozF0aBx+Ph5Rde5tCuIgI0gdi9VvLm5/KFL90vN38/JwlucckNDAwQHKQMC22AqMhAisvb\ngcG1Kvbt20dEcB9TsvIAcDjc7PjwBNPSW8jNjCTI1Me7bxfSPncDS5ZcfdF1hISE8OWv/IQDB/bw\nwb5SgkNSufXOq6+Ira/Gksfj4ciRI7z4/EvUFjWyZPbVxMbGoqoqJw8cZ2v0Nm65df14lzmpSXCL\nSy4iIoJ+qx6z2UZY2MfjyDW1ZhKSZlNSUsK7256nz1xLT2c1RqOFddfnc/xkM9GRFubOisarBJKe\nnkBaSgT/+9dNFBTM/0xPXwYHB7N69fXA9aPYwiuXz+fjqb88TcXBaspKqohREzl24Djp0/qZOnUK\nUxKnsXv7HtbfcrPMFPkcZORfXHIGg4Ely27lpU2nqKhqp6NzgN37ajlWaiA1NYt33nqMO9cF8X++\nM4c71kcRZupg0xuHaWhsY1pWAB2d3qF9BYOD/YiNVIetBy7GT2VlJeWHq5iVXoBRZyTCFElsSDy1\nlbXY7Db0Oj0up2tcHrS6nEiPW4yLRYuWEhISzsFD27EM9JCcchUPfvka9uzezsK5ASTEhwIQG5eN\nuauKfYdqCQqKxmHrZt7cPEJDB28eqqpKb7+HoKCg8WyOOKO6qppgXSgaRUNSQhKnaxoIM0bidfro\nNffiUpzk5efKPYTPSYJbjJvc3FymTJlCaWkpzc31lJeX0d3VQnbyx0MeWVlT6QqLRPvBITya2Zw6\nfYrr1qQCg7+W79lfjyl0KtHR0ePUCvFJQaYg3D4XHq8Hq81CeccJgjxhqF4fPfs6mLEsh4dv/8J4\nlznpSXCLcWOz2Xj2mUcJ9j9NRqo/HU0uCgs7MGoCmZIVM3Se0RhEQHAW3/3+v1JVVcULrz9PkH8r\nVpuXyJhc7rzrARkvnSDy8/N55a+vsXH7cbpbepidOJ8+ixmrb4CohEhyZkyV6X6jQIJbjJvduz8k\nOaaZtaunDgVvTLSBvzxbRkhwILk5kfQPONi9v4eFi+/C39+fmTNnMn36f9PR0YGfn9/QWLe4tFpb\nWzl58iRtbW0kJycze/ZsQkJCqKmpwWlz0XqqgwCPiQpLKcGRJm5fdyd+/n4cP1KIx+NBp5Po+Tzk\n0xPjprL8IHfcFDestzw3P5l3tnez9QM7v3/8b/i8KslpBVyz9uMnMXU6HfHx8eNRsgA++vAjXnrq\nVWrL63AOuEBRiMmI4N6H72b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EGsSA3WjH6/Vy+x1f5vH/2cL+A7vo8/sZNPVz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\nxK1pmhZj/hdxQkV4VifhNQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc249ae1630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OqaqKZ9BKUFDQhSpbiK8sMDCQnj7vacd7et2YQyZfg0OCW4xgMBj47re+RXNz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\nuw/Nn40AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc24907cd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "agglo_euclidean = AgglomerativeClustering(n_clusters=3, affinity=\"euclidean\", linkage=\"complete\").fit_predict(X)\n",
    "agglo_manhattan = AgglomerativeClustering(n_clusters=3, affinity=\"manhattan\", linkage=\"complete\").fit_predict(X)\n",
    "\n",
    "# Usando metodo euclidean\n",
    "\n",
    "f, ax = plt.subplots()\n",
    "ax.scatter(data_df[0], data_df[1], c=agglo_euclidean, alpha=0.5, edgecolor='k')\n",
    "plt.show()\n",
    "\n",
    "f, ax = plt.subplots()\n",
    "ax.scatter(data_df[0], data_df[1], c=y, alpha=0.5, edgecolor='k')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YNuQ8nVaHmUAaGhokuMWoUhSFtLS0wbD+rIaGBvSREYOh/cn5lrh4qo4fH3PB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\nLF9beS1BKcF09XXywsMvM2FaGlkRk8j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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc249b0f940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OqaqKZ9BKUFDQhSpbiK8sMDCQnj7vacd7et2YQyZfg0OCW4xgMBj47re+RXNz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\nuw/Nn40AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc2511bffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# usando metodo manhattan\n",
    "f, ax = plt.subplots()\n",
    "ax.scatter(data_df[0], data_df[1], c=agglo_manhattan, alpha=0.5, edgecolor='k')\n",
    "plt.show()\n",
    "\n",
    "f, ax = plt.subplots()\n",
    "ax.scatter(data_df[0], data_df[1], c=y, alpha=0.5, edgecolor='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
